Light-shift modulated photon-echo

HAL Id: hal-01323975

https://hal.archives-ouvertes.fr/hal-01323975

Submitted on 31 May 2016

HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Light-shift modulated photon-echo

Thierry Chanelière, Gabriel Hétet

To cite this version:

Thierry Chanelière, Gabriel Hétet. Light-shift modulated photon-echo. Optics Letters, Optical Society

of America - OSA Publishing, 2015, 40 (7), pp.1294. �10.1364/OL.40.001294�. �hal-01323975�

arXiv:1501.05411v2 [quant-ph] 24 Feb 2015

Thierry Chaneli` ere

and Gabriel H´ etet

1

Laboratoire Aim´ e Cotton, CNRS, Universit´ e Paris-Sud and ENS Cachan, CNRS-UPR 3321, 91405 Orsay, France

2

Laboratoire Pierre Aigrain, Ecole Normale Sup´ erieure-PSL Research University, CNRS, Universit´ e Pierre et Marie Curie-Sorbonne Universit´ es,

Universit´ e Paris Diderot-Sorbonne Paris Cit´ e, 24 rue Lhomond, 75231 Paris Cedex 05, France

compiled: February 25, 2015

We show that the AC-Stark shift (light-shift) is a powerful and versatile tool to control the emission of a photon-echo in the context of optical storage. As a proof-of-principle, we demonstrate that the photon-echo efficiency can be fully modulated by applying light-shift control pulses in an erbium doped solid. The control of the echo emission is attributed to the spatial gradient induced by the light-shift beam.

OCIS codes: (020.1670); (160.5690); (160.2900); (210.4680); (270.5565); (270.5585) http://dx.doi.org/10.1364/XX.99.099999

The photon-echo technique has been reconsidered re- cently with important applications in the context of quantum information storage and processing [1]. The two-pulse or three-pulse schemes have inspired a vari- ety of storage protocols [2]. The echo techniques have been implemented in different systems from atomic va- pors to doped solids with remarkable performances in terms of efficiency [3, 4], bandwidth [5], multiplexing capacity [6, 7]. The two-pulse echo is indeed a stim- ulating source of inspiration to propose new protocols.

In the echo sequence, the classical π-pulses must be as- sociated with an extra control parameter to make the protocol suitable for quantum storage. This can be a rapidly switched electric field [8–11], a magnetic field [12–14], a modified phase-matching condition [15] or a frequency tunable active cavity [16, 17].These propos- als cover different realities, atomic vapors and doped solids, both in the optical or the radio-frequency domain.

The AC-Stark shift or light-shift can naturally complete this panoply for materials with a weak or zero sensitiv- ity to the DC-Stark or Zeeman effects as pointed out early by Kraus et al. [9]. As a counterpart of the DC- Stark shift which has already proven to be very efficient for quantum memories based on the so-called gradient echo protocol [4], the light-shift is considered because of its versatility for the gradient design [18] and its fast switching time [19]. The imprinted phase pattern can also apply for optical memories based on “electromag- netically induced transparency” [20]. This latter result demonstrates the deflection of the retrieved signal which is clearly a possibility offered by the light-shift gradi- ent design. The shift induced by strong laser pulses on spin transitions (electronic and/or nuclear) is also used in spin-echo sequences showing the omnipresence of the phenomenon in different fields [21–23].

Within this general framework, we investigate experi- mentally the use of light-shift pulses in a standard two- pulse photon-echo sequence. We show that the emission can be fully modulated by applying light-shift pulses.

Our demonstration is in that sense equivalent to the DC-Stark shift modulated spectroscopy pioneered by Meixner et al. [24]. In our case, we attribute the mod- ulation to the phase spatial pattern imprinted on the coherences by the light-shift beam. This phase gradi- ent is a starting point to realize an all-optical version of the gradient-echo memory [19, 25]. We first show that the emission of a two-pulse photon-echo (2PE) in Er

:Y

SiO

can be controlled by applying a strong off- resonant pulse. The latter produces a light-shift during the free evolution of the coherences partially inhibiting the echo emission later on. We compensate this extra dephasing by a second light-shift pulse thus validating the method for controlling the emission of an optical memory.

We choose Er

:Y

SiO

as a test-bed for the light- shift modulated photon-echo experiment because it is re- calcitrant to the efficient implementation of the gradient- echo scheme with DC-Stark shifts [26]. Our experimen- tal setup has been extensively described previously in refs.[27, 28] (see Fig.1). We implement a 2PE sequence in Fig.2 with a probe beam polarized along D

whose waist is 50 µm. Its Rabi frequency is 2π × 150kHz mea- sured by an optical nutation experiment [29]. There is no preparation of the medium by optical pumping.

The sequence is repeated every 20ms so the atoms are all initially in the ground state. The 2PE is composed of two gaussian 1µs pulses (rms-duration) separated by t

= 35µs. The echo is observed at 2t

= 70µs (Fig.2).

A second beam is used to produce off-resonant excita-

tion (light-shift pulse) within the echo sequence. The

2 latter has a waist of 110 µm and is polarized along D

.

Its Rabi frequency is Ω

≃ 2π × 330kHz. It is counter- propagating and overlapped with the probe beam.

Fig. 1. Y

SiO

sample doped with 50 ppm of Er

. At 1.8 K and under a 2T magnetic field in the plane (

-

), the coherence time is

130µs (

I

-

I

transition for “site 1” ) [28, 30].

0 10 20 30 40 50 60 70 80

0 0.5 1 1.5 2 2.5 3

Intensity (arb.u.)

Time (µs)

0 0.5 1

0 0.2 0.4 0.6 0.8 1

Echo intensity

ILS/ILS^max Light−shift pulse

1.5MHz

Fig. 2. Two-pulse photon echo sequence (dashed black line).

We apply two strong pulses at

= 0 and

= 35µs (clipped by the oscilloscope scale). We observe an echo at 2t

= 70µs.

The intensity is normalized so that the echo amplitude is 1.

When a light-shift pulse detuned by 1.5MHz (in solid red) is applied at

is reduced from 100% to 30%. Inset: Reduction of the echo intensity as a function of the light-shift intensity

(the dashed line is used to guide the eye). Measurement errors are a few percents given by shot-to-shot fluctuations due to the laser jitter (they roughly correspond to the markers size).

In Fig.2, we show that when a light-shift pulse whose rms-duration τ = 3µs and detuned by ∆ = 2π × 1.5MHz is applied at

t

= 17.5µs, the echo is reduced from 100% to 30%. In Fig.2 (inset), we also increase gradually the light-shift pulse intensity I

from 0 to its maximum value I

corresponding to Ω

.

The destruction of the echo by an extra pulse inserted in the time sequence is not obviously attributed to the light-shift induced on the coherence rephasing. Never- theless it should be noted that the light-shift beam is sufficiently detuned to produce only an off-resonant ex- citation on the atoms driven by the probe. The probe

pulses have a duration of 1µs so their bandwidth is typ- ically 150kHz very comparable to the Rabi frequency of 2π × 150kHz. This is significantly lower than the light- shift beam detuning 1.5MHz.

We now investigate the light-shift dependency as a function of the experimental parameters. If the light- shift pulse is described by its time-varying Rabi fre- quency Ω(t), one expects the transition of the atoms under the probe to be shifted by

. The accumu- lated phase Φ

is then

Φ

= Z

t

Ω

(t)

∆ dt = √ 2π Ω

∆ τ (1)

given by the gaussian pulse parameters, Ω

its ampli- tude and τ its duration. We investigate this dependency (Eq.1) by first varying ∆. The time sequence is the same as before (see Fig.2) expect that τ = 2µs and ∆ is varied from 2π × 1MHz to 2π × 3MHz.

1 1.5 2 2.5 3

0 0.2 0.4 0.6 0.8 1

Echo intensity

Detuning∆/(2π) (MHz)

Fig. 3. Echo intensity when the light-shift pulse detuning ∆ is varied (square symbols). The experiment is repeated by varying ∆ but by keeping

goes from 2µs to 6µs (circles). The dashed lines are used to guide the eye. Measurement errors are again a few percents.

When ∆ is increased (Fig.3), the effect of the light- shift pulse is reduced, thus qualitatively following the 1/∆ dependency. A quantitative analysis is not directly possible because a perturbative treatment is inappropri- ate when strong pulses are used [29]. Alternatively, we propose to vary ∆ but by keeping τ /∆ constant to val- idate Eq.(1). In this latter case, we observe that the effect of the light-shift is quasi-constant. A weak sig- nificant variation from 30% to 38% is still observable.

It cannot be explained by Eq.(1). Additional modeling would be required but the agreement with the expected τ /∆ dependency is satisfying.

To further explore this effect, we now propose to apply

a first phase shift within the sequence and to compen-

sate it by a second pulse. Looking at Eq.(1), an intuitive

compensation solution is to apply two successive pulses

with opposite detunings during the free evolution be-

tween t = 0 and t

. A less obvious solution offered by

the 2PE sequence is to apply one light-shift pulse be-

tween t = 0 and t

(called region I) and a second one

between t

and 2t

(called region II) with the same detuning. To justify this compensation scheme, we can simply track down the accumulated phase φ(ω, t) due to the inhomogeneous dephasing [29]: (i) In region I, after the first excitation, the coherence at the frequency ω freely evolves, accumulating φ(ω, t) = ωt. Just before the second pulse at t

, the phase is φ(ω, t

) = ωt

. (ii) If a light-shift pulse is applied in region I, an extra term Φ

is added: φ(ω, t

) = ωt

+Φ

. (iii) The sec- ond pulse conjugates the coherence so the phase is now φ(ω, t

) = − ωt

− Φ

right after the second pulse.

(iv) During the free evolution from t

to t in region II, the accumulated phase is ω(t − t

) so the total phase is φ(ω, t) = − ωt

− Φ

+ ω(t − t

) = ω(t − 2t

) − Φ

. As expected, the retrieval time 2t

corresponds to the coherence rephasing. (v) If a light-shift pulse is applied in region II, an extra term Φ

is added. Thus the total inhomogeneous phase at the instant of retrieval is

φ(ω, t) = ω(t − 2t

) − Φ

+ Φ

. (2) As a conclusion, similar pulses (same detuning) applied in region I and II compensate each other. Pulses with opposite detunings cancels each other only if they are both in region I or II exclusively. As we see in Fig.4, by properly choosing the sign of the detuning and the region of application, we can retrieve an echo with 98%

(Fig.(4.a) and (4.c)) of its initial reference intensity.

As a summary, the dependency as τ /∆ illustrated in Fig.3 and the compensation scheme presented in Fig.4 based on Eq.(2) is a strong evidence that the echo is indeed controlled by the light-shift induced by the off- resonant pulses. This analysis justifies the main claim of our paper. Even if we have shown that the induced light-shift can be used to fully modulate the echo from 100% to 3% (Fig.4.d), a quantitative link between Eq.(1) and the echo amplitude including gaussian propagation effects is not obvious. In a first approach, the echo am- plitude is the total contribution of the excited atoms (at frequency ω) at a given position R leading to an emission in the k direction proportional to [29]:

X

ω, ~R

exp (k.R − k

.R + φ(ω, t)) (3) where k

is the probe wave-vector. The inhomogeneous phase φ(ω, t) may also include a spatial dependency if the light-shifts depend on R. Without light-shift, the echo peaks in the k

direction (phase-matching) at t = 2t

(eq.2). It is important to note that a net global added phase to all the atoms excited by the 2PE does not change the echo amplitude but only its phase.

The echo is reduced only if the phase varies through the inhomogeneous profile (depends on ω, spectral depen- dency) or is not constant through the sample (R, spatial dependency). A spectral dependency may prevent the coherence rephasing at t = 2t

. A spatial dependency modifies the phase-matching condition when the echo is emitted. We discuss these two possible effects before concluding.

0 1

2 +1.5 MHz

−1.5 MHz

0.98

(a)

0 1 2

+1.5 MHz +1.5 MHz

0.06

(b)

0 1

2 +1.5 MHz +1.5 MHz

0.98

(c)

0 20 40 60 80

0 1

2 +1.5 MHz −1.5 MHz

0.03

(d)

Intensity (arb.u.)

Time (µs)

Region I Region II

Fig. 4. Light-shift pulses compensation scheme. (a) If two pulses with opposite detunings are applied in region I, the echo intensity is 98% of its initial value. (b) With the same detuning, the effect of the light-shift is cumulative and the echo is only 6%. When applied in region I and II respectively, the pulses compensate each other with the same detuning (98% echo intensity in (c)) or add up with opposite detun- ing (3% echo intensity in (d)). The light-shift pulses have a

±

1.5MHz detuning and a

= 3µs duration (as in Fig.2).

A spectral dependency induced by the light-shift has a negligible influence in our case because the detuning is significantly larger than the excited bandwidth as previ- ously mentioned. It should be noted that the first order effect of a spectral dependency described by

Φ

(ω) = √

2π Ω

∆ + ω τ ≃ √ 2π Ω

∆ τ − √ 2π Ω

∆

τ ω (4) is to modify the retrieval time from 2t

to 2t

±

√ 2πτΩ

/∆

(see Eq.2 depending if the pulse is in re- gion I or II). The pulse should be delayed to the first order. This is not what we observe so the spectral de- pendency is certainly negligible.

The spatial dependency of the induced light-shift

Φ

(z, r) can now be discussed. It may be both lon-

gitudinal (along z) and transverse (along r, in the (x, y)

plane). We choose to overlap the probe and light-shift

beams, as a consequence the longitudinal and transverse

gradients are decoupled (rotational symmetry). It sim-

plifies our analysis at this level. Nevertheless, we have

also verified experimentally that angled beams produces

a significant reduction of the photon-echo. It should be

kept in mind when more practical conditions are con-

sidered. In our case, the z-gradient may be due to the

absorption of the light-shift beam Ω

(z) along the prop-

agation direction z. The r-gradient appears because the

4 light-shift beam as a finite size (110 µm) with respect

to the probe (50 µm). The longitudinal dependency can be evaluated. At z = 0, we have Ω

(0) ≃ 2π × 330kHz and then Φ

(0) ≃ 1.1π. The gaussian divergence of the light-shift beam is negligible because its Rayleigh length is ten times longer than the crystal. On the contrary, its complete absorption would produce a phase gradient from 1.1π at z = 0 to 0π at the output of the sample.

In other words, the input and the output slice emissions would be out of phase thus explaining the echo reduc- tion (phase mismatch). This appealing explanation is unfortunately extremely unlikely. The medium is ab- sorbing for the light-shift beam which is polarized along D

(optical depth ∼ 3.5). Nevertheless, the light-shift pulses area is large ( ∼ 7π) so they are not absorbed as small-area pulses would be [29]. They may exhibit soli- tonic propagation or self-induced-transparency, in any case their amplitude will not go to zero. We have per- formed 1D-Bloch-Maxwell numerical simulations mod- eling the echo emission and the light-shift pulse prop- agation along z thus taking into account the spectral and the longitudinal spatial dependency. We could not simulate the echo reduction but only the modified echo retrieval time by √

2πτ Ω

/∆

which is not the domi- nant experimental observation anyway. The simulated light-shift pulse propagation qualitatively corresponds to the experimental outgoing shape predicting a negligible

∼ 3% absorption for a 7π area pulse. The transverse spatial dependency is a very likely explanation. A first order estimation of the transverse shift induced by the probe (50 µm) and light shift beam (110 µm) spatial mode mismatch only predicts a 10% echo modulation.

3D-Bloch-Maxwell numerical simulations would be nec- essary to account for the three-dimensional propagation of the echo.

To conclude, we show that the photon echo emission can be fully modulated by applying off-resonant pulses within the time sequence. The echo is modified by the transverse spatial phase gradient imprinted by the light- shift beam on the atomic coherence.. It is a powerful and versatile tool to manipulate the emission of quan- tum memories. We obtain very comparable results with a Tm

:YAG sample showing the entirety of the phe- nomenon. Our demonstration opens up new perspec- tives for materials with a low Stark or Zeeman sensitiv- ity.

We have received funding from the Marie Curie Ac- tions of the European Union’s 7th Framework Pro- gramme under REA no. 287252, from the national grants ANR-12-BS08-0015-02 (RAMACO) and ANR- 13-PDOC-0024-01 (retour post-doctorants SMEQUI).

References

[1] F. Bussi`eres, N. Sangouard, M. Afzelius, H. de Riedmatten, C. Simon, and W. Tittel, J. Mod. Opt.

, 1519 (2013).

[2] W. Tittel, M. Afzelius, R. Cone, T. Chaneli`ere, S. Kr¨ oll, S. Moiseev, and M. Sellars, Laser Photon. Rev.

, 244 (2010).

[3] M. Hosseini, B. M. Sparkes, G. Campbell, P. K. Lam, and B. C. Buchler, Nat. Commun.

, 174 (2011).

[4] M. P. Hedges, J. J. Longdell, Y. Li, and M. J. Sellars, Nature

, 1052 (2010).

[5] E. Saglamyurek, N. Sinclair, J. Jin, J. A. Slater, D. Oblak, F. Bussieres, M. George, R. Ricken, W. Sohler, and W. Tittel, Nature

, 512 (2011).

[6] M. Bonarota, J.-L. L. Gou¨et, and T. Chaneli`ere, New J. Phys.

, 013013 (2011).

[7] N. Sinclair, E. Saglamyurek, H. Mallahzadeh, J. A.

Slater, M. George, R. Ricken, M. P. Hedges, D. Oblak, C. Simon, W. Sohler, and W. Tittel, Phys. Rev. Lett.

, 053603 (2014).

[8] M. Nilsson and S. Kr¨ oll,

Optics Comm.

, 393 (2005).

[9] B. Kraus, W. Tittel, N. Gisin, M. Nilsson, S. Kr¨ oll, and J. I. Cirac, Phys. Rev. A

, 020302 (2006).

[10] G. H´etet, J. Longdell, A. Alexander, P. Lam, and M. Sellars, Phys. Rev. Lett.

, 023601 (2008).

[11] D. L. McAuslan, P. M. Ledingham, W. R. Naylor, S. E.

Beavan, M. P. Hedges, M. J. Sellars, and J. J. Longdell, Phys. Rev. A

, 022309 (2011).

[12] Y. Wang, D. Boye, J. Rives, and R. Meltzer, J. Lumin.

45

, 437 (1990).

[13] G. H´etet, M. Hosseini, B. M. Sparkes, D. Oblak, P. K.

Lam, and B. C. Buchler, Opt. Lett.

, 2323 (2008).

[14] G. H´etet, D. Wilkowski, and T. Chaneli`ere, New J. Phys.

, 045015 (2013).

[15] V. Damon, M. Bonarota, A. Louchet-Chauvet, T. Chaneli`ere, and J.-L. Le Gou¨et, New J. Phys.

, 093031 (2011).

[16] B. Julsgaard, C. Grezes, P. Bertet, and K. Mølmer, Phys. Rev. Lett.

, 250503 (2013).

[17] M. Afzelius, N. Sangouard, G. Johansson, M. U. Staudt, and C. M. Wilson, New J. Phys.

, 065008 (2013).

[18] G. H´etet and D. Gu´ery-Odelin,

arXiv:quant-ph/1501.01194.

[19] B. M. Sparkes, M. Hosseini, G. H´etet, P. K. Lam, and B. C. Buchler, Phys. Rev. A

, 043847 (2010).

[20] U. Schnorrberger, J. D. Thompson, S. Trotzky, R. Pugatch, N. Davidson, S. Kuhr, and I. Bloch, Phys. Rev. Lett.

, 033003 (2009).

[21] M. Rosatzin, D. Suter, and J. Mlynek, Phys. Rev. A

, 1839 (1990).

[22] T. Moriyasu, Y. Koyama, Y. Fukuda, and T. Kohmoto, Phys. Rev. A

, 013402 (2008).

[23] J. Berezovsky, M. H. Mikkelsen, N. G. Stoltz, L. A. Col- dren, and D. D. Awschalom, Science

, 349 (2008).

[24] A. Meixner, C. Jefferson, and R. Macfarlane, Phys. Rev. B

, 5912 (1992).

[25] W.-T. Liao, C. H. Keitel, and A. P´ alffy, Phys. Rev. Lett.

, 123602 (2014).

[26] B. Lauritzen, J. c. v. Min´ aˇr, H. de Ried-

matten, M. Afzelius, and N. Gisin,

Phys. Rev. A

, 012318 (2011).

[27] J. Dajczgewand, J.-L. Le Gou¨et, A. Louchet-Chauvet, and T. Chaneli`ere, Opt. Lett.

, 2711 (2014).

[28] J. Dajczgewand, R. Ahlefeldt, T. B¨ ottger, A. Louchet- Chauvet, J.-L. L. Gou¨et, and T. Chaneli`ere, New J. Phys.

, 023031 (2015).

[29] L. Allen and J. Eberly, Optical resonance and two-level atoms (Courier Dover Publications, 1987).

[30] T. B¨ ottger, C. W. Thiel, R. L. Cone, and Y. Sun,

Phys. Rev. B

, 115104 (2009).